Exciton Formation Entropy Changes in Transition Metal Dichalcogenide Atomic Layers.

The atomic layers of transition metal dichalcogenides (TMDCs, MX2; M = Mo or W; X = S, Se, or Te) are of great interest in the areas of photonics and optoelectronics due to the correlation between valley orbital, spin, and optical helicity; the compositional tuning of exciton bandgaps in visible and near-infrared spectra; and the bandgap modification from indirect for bilayer or multilayer to direct for monolayer. The derivative of the O'Donnell and Chen relation is analyzed as a function of temperature and gives the relationship between the change in entropy of exciton formation and the bandgap energy. The analysis suggests the change in entropy of exciton formation with higher energy phonons (100 meV) is constant until ~90 K while lower energy phonons (10 meV) approaches a constant value of -2skB between ~250 K and ~300 K where s is the strength of electron-phonon interaction and kB is the Boltzmann constant. Increased scattering and spontaneous decay probabilities explains the amplified electron-phonon interaction when the phonon energy is large. The change in exciton formation entropy can be increased ~3-fold while the bandgap is managed through the electron-phonon coupling strength.